Eindopdracht

library(deSolve)
library(pracma)

## 
## Attaching package: 'pracma'

## The following object is masked from 'package:deSolve':
## 
##     rk4

library(plotly)

## Loading required package: ggplot2

## 
## Attaching package: 'plotly'

## The following object is masked from 'package:ggplot2':
## 
##     last_plot

## The following object is masked from 'package:stats':
## 
##     filter

## The following object is masked from 'package:graphics':
## 
##     layout

r <- 0.11
rho <- 1.29
c <- 0.5

parameters <- c(m = 0.445, k = (1/2) * c * rho * (pi * r^2),
                mu = 0.1, g = c(x = 0, y = -9.81))

v <- 30
state_straight <- c(velocity = c(x = v*cos(15*pi/180), y = v*sin(15*pi/180)),
                    position = c(x = 0, y = 0))

times <- seq(0, 10, by = 0.01)

model <- function(t, y, parms){
  with(as.list(c(y, parms)), {
    g <- c(g.x, g.y)
    velocity <- c(velocity.x, velocity.y)
    position <- c(position.x, position.y)
    
    acc <-  (m * g - k * velocity * sqrt(velocity.x^2 + velocity.y^2)) / m 
    
    return(list(c(acc, velocity)))
  }
  )
}


out <- as.data.frame(ode(times = times, y = state_straight, parms = parameters, func = model, method = "euler"))
output <- subset(out, position.y > 0)
output$position.z <- rep(0, length(output$time))

plot(output$position.x, output$position.y, type = "l")

fig <- plot_ly(output, x = ~position.z, y = ~position.x, z = ~position.y, type = 'scatter3d', mode = 'lines',
        opacity = 1)
fig